This work proposes a new modeling framework based on combining graded band-gap (GBG) engineering and metaheuristic optimization to improve the Cd-Free ZnMgO/CIGS solar cell performances. Analytical and numerical calculations are carried out to assess the influence of band-gap profiles of both buffer and active layers on the electronic and optical properties of the studied solar cell. This investigation shows a great improvement of solar cell efficiency by increasing the optoelectronic figures of merit through tuning and optimizing the band-gap profiles and the conduction band offset at the ZnMgO/CIGS interface. Moreover, metaheuristic-based optimization models are developed to optimize the GBG profiles and enhance the optical and electrical performances of the solar cell. In this context, we recorded very satisfactory results, where the optimized design with GBG paradigm offers a high efficiency of 31.88% compared to 23.35% provided by the conventional CdS/CIGS solar cell. Therefore, this study provides a new strategy in enhancing the efficiency of thin-film solar cells by exploiting the graded band-gap engineering combined with metaheuristic optimization approach.